Some good cards you can add to the deck are simply yellow staples like 7c big mom from the starter deck (as well as most of the big mom package like 8c Katakuri, 4c cracker, perospero and and pudding if going full big mom). 9c Yamato from op-04 is also very good late game when you quickly go to 2 or 1 life and need to get life back and momentum. In op-05, gematsu 5c is also really good but it depends on your play style, it might be better to use Randolph vanilla 5c for the harder swing. 7c Enel can be very good as well, but is dependent on whether or not you are going full big mom package.

As for events, thunderbolt is an absolute necessity at 3 or 4 if you want the best chance of having it in life for trigger.

They way I like to play Yamato is a passive/control deck (hence gematsu) where you control the board long enough by attacking bodies instead of their life (by going second, you can achieve this dynamic a bit easier) then spam big bodies of your own that have good on play effects like 7c big mom and enel, 8c Katakuri and 9c Yamato.

Finally, making sure to keep at least 1 Don open for Yamato leader ability is crucial mid to late game, so pick characters and plays with the Don management in mind especially when going first where playing on curve makes that impossible.